Learning Blender. Add custom hyperlink button to UI to navigate to browser
You can use bpy.ops.wm.url_open() to open a url from a button.

For example, using the UI Panel Simple template (from the Text Editor> Templates> Python) you can add this to the draw method:

def draw(self, context):
    layout = self.layout
    row = layout.row()
    row.operator("wm.url_open", text="Open Link").url = "http://www.google.co.uk"


This will display a button whose sole purpose is to open a link. If you already have a button and just want to add this extra functionality, you can call the operator directly with:

bpy.ops.wm.url_open(url="http://www.google.co.uk")